Thread: Complex Conjugation Vector Space

Can someone help me with this vector proof?

Let V be the set of all complex-valued functions f on the real line such that (for all t in R)
f(-t)=f(t) bar (the bar denotes complex conjugation)
Show that V, with the operations
(f+g)(t) = f(t) + g(t)
(cf)(t) = cf(t)

is a vector space over the field of real numbers.

Originally Posted by krepka

Can someone help me with this vector proof?

Let V be the set of all complex-valued functions f on the real line such that (for all t in R)
f(-t)=f(t) bar (the bar denotes complex conjugation)
Show that V, with the operations
(f+g)(t) = f(t) + g(t)
(cf)(t) = cf(t)

is a vector space over the field of real numbers.

You basically need to show that if and .
Just follow the definitions here.